The signal of the GNSS satellites can be used to estimate the amount of water vapor in the atmosphere. For this reason, GNSS observations are nowadays routinely used by several meteorological institutes (e.g., MetOffice, Meteo France) to monitor weather events and to improve their weather forecasts quality. The analysis of a whole network of GNSS stations to estimate a full three-dimensional model of the water vapor content is a challenging and computationally demanding task. For this purpose, a tomographic system SEGAL GNSS Water Vapour Reconstruction Image Software (SWART) was developed and tested. The new method makes use of parallelized algebraic reconstruction techniques (ARTs) and supersedes other implementations in terms of speed by at least 50% for small networks. For SWART, the computation time grows linearly with the number of observations. As a result, the new method makes possible to estimate the water vapor for larger GNSS networks and can be used for near-real-time weather predictions. To show its potential, data from 26 stations in Poland were analyzed using data from a period of 56 days. Good agreement in the estimated water vapor between SWART and radiosondes solutions was obtained, with a mean RMS of 1.5 g/m³ for the lower layers and an overall improvement of 5% until the layer 6750 m when compared with the atmospheric model (WRF). Furthermore, rapid and strong variations observed by radiosondes were not modeled by the WRF but were detected by GPS tomography.